1 Answer
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ON BOTTOM:
You're probably in the danger zone. You need to either be all the way out, or all the way in. Hanging out in-between is going to get you darce'd or passed. And you should never be flat on your back whether you are all out or all in. If you are all the way out, you should be working on obtaining the under-hook which will work to allow you to take the back. If you move to take the back, don't do a sit-up, instead, take the free leg and kick it / stomp it which will give you momentum when rising up.

Now if you are playing a deep-half, you want to be on your side, as tight to them as possible, and as much under their hips as possible. Again, look for the under-hook either on their back or around their legs if attempting the deep-half sweep. If you go for the sweep, you would work to clasp your hands together, one around the trapped leg, and the other around the leg closest to your head, and then drive into them while coming up to your knee's keeping your opponents leg trapped with your legs. This is very nice sweep that will allow you to transition to a knee-bar or move right into passing once you are on top.

If you are playing deep-half and don't feel comfortable getting the sweep, you can attempt the sweep and as they move to crush you back down you then roll HARD away from your opponent (you must have the underhook at their mid-back level), and complete the sweep.

If you don't want to sweep or don't feel comfortable making that move; then when in the deep-half, you can transition to x-guard, or work your way out the back-door (through their legs) completely.

If your opponent attempts a standing half-guard pass or the back-step pass you can move to de la hiva guard or even a spider-guard if you can hip and catch the transition fast enough. Also, if they attempt a back-step pass, you can shift away from them as they back-step and then post with your bottom arm, and come up into them, and get on top. This will put you in a good position to pass as-well.

ON TOP:

Flatten them out. That eliminates most of their options. If they are stubbon and won't flatten, threaten the darce choke if they give it to you. Or a half-guard ezekiel choke. Or a keylock. Or you can at higher belt levels, threaten a slew of leg-lock techniques. If I have someone sbeing lazy in half-guard I will usually pull them in a bit closer and take my non-trapped leg, and wrap it around their head. Then I'll drop my weight on their head with a nice squeeze of my leg. I tend to land a keylock from there as a nice bonus. Or you can look for bow and arrow chokes from the top half-guard position, they are everywhere and you don't even need to have that trapped leg untrapped.

Now in terms of passing, you want to keep them flattened, and work to get your far-side under-hook and then work the knee-slicer pass. If you feel unable to get the under-hook then you can wrap the head but be advised, most legit jiu-jitsu fighters will take your back if you attempt to wrap only the head.

You can perform a back-step pass, where you do a back-step across their body, and while balancing your weight on them and yet also being extremely stable, you can then use your left hand to secure their knee and work your trapped leg free and then complete the pass.

You can also always place your opponent in a flattened-out position, and attempt a ninja-roll.

You can flatten out your opponent, and achieve an underhook on the far side. Reach up and grab their shoulder and clamp down on it. You want their back to stiff and rigid you are clamping down so hard. Then place your head on the mat above their shoulder that is nearest to you, right next to your opponents ear. Then step out a bit to your trapped side, and drop your hips a small bit while turning a tiny bit away from your opponent. Then take your non-trapped leg, and use your hook to push against their deep-half outer-most hook, and then you can slowly slide your knee out. Your leg will be straight all the way while it slides out. This is a great pressure pass once you get very good at it, but depending on your length, this can feel pretty twingy on that trapped knee. I like it though but again, it's one that leaves you wondering if it'd be possible to hurt yourself while attempting this pass.

Just look into some of the key terms I've tried to use and then practice, practice, practice. I don't have names for all my passes either, sorry. There are so many moves from here, just pick 3-4 that you really like, and then work those.

Forgive my spelling mistakes, it's so late the screen is getting blurry! If I have time tomorrow I'll come in and add in some video links, but it's just too late right now.